$\overline{AB}$ = $8\sqrt{2}$ $\overline{AC} = {?}$ $A$ $C$ $B$ $8\sqrt{2}$ $?$ $ \sin( \angle ABC ) = \frac{ \sqrt{2}}{2}, \cos( \angle ABC ) = \frac{ \sqrt{2}}{2}, \tan( \angle ABC ) = 1$
Solution: $\overline{AB}$ is the hypotenuse $\overline{AC}$ is opposite to $\angle ABC$ SOH CAH TOA We know the hypotenuse and need to solve for the opposite side so we can use the sine function (SOH) $ \sin( \angle ABC ) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{\overline{AC}}{\overline{AB}}= \frac{\overline{AC}}{8\sqrt{2}} $ $ \overline{AC}=8\sqrt{2} \cdot \sin( \angle ABC ) = 8\sqrt{2} \cdot \frac{ \sqrt{2}}{2} = 8$